scholarly journals Lie symmetry analysis and invariant solutions for (2+1) dimensional Bogoyavlensky-Konopelchenko equation with variable-coefficient in wave propagation

2021 ◽  
Author(s):  
Mohamed R. Ali ◽  
Wen-Xiu Ma ◽  
R. Sadat
Keyword(s):  
Wave Propagation ◽  
Variable Coefficient ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Invariant Solutions ◽  
Lie Symmetry Analysis

scholarly journals Lie Symmetry Analysis and Invariant Solutions of a Nonlinear Fokker-Planck Equation Describing Cell Population Growth

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Jia Zheng
Keyword(s):  
Planck Equation ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Power Series Solution ◽  
Invariant Solutions ◽  
Lie Symmetry Analysis ◽  
Fokker Planck Equation ◽  
Growing Cell ◽  
Cell Population Growth ◽  
Fokker Planck

In this paper, a complete Lie symmetry analysis is performed for a nonlinear Fokker-Planck equation for growing cell populations. Moreover, an optimal system of one-dimensional subalgebras is constructed and used to find similarity reductions and invariant solutions. A new power series solution is constructed via the reduced equation, and its convergence is proved.

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